Abstract Algebra: Theory and Applications · Problem 41

Permutation Groups — Thomas Judson

Mathematics — Abstract Algebra · complex-numbers-polar

Problem

z = r(\cos\theta + i\sin\theta)

and

w = s(\cos\phi + i\sin\phi)

are two nonzero complex numbers, show that

zw = rs[\cos(\theta+\phi) + i\sin(\theta+\phi)].